MUTUAL COVERINGS OF CONES OF MONOTONE FUNCTIONS AND ESTIMATES OF THEIR INTEGRAL MAJORANTS

Bakhtigareeva E.G. Goldman M.L. Karshygina G.Z.
April 2023 Springer

Journal of Mathematical Sciences (United States)
2023 #271 Issue 6 714 - 732 pp.

Questions of mutual covering and equivalence of cones of monotone functions and the corresponding estimates of their majorants are studied. Two types of coverings are considered: pointwise and integral. They correspond to pointwise and integral estimates of the majorants on these cones. The results obtained are used to derive formulas that allow estimating pointwise and integral majorants of decreasing rearrangements for generalized Riesz and Bessel potentials.

Cones of decreasing rearrangements of potentials , Cones of monotone functions , Generalized Riesz potentials , Integral majorants on cones , Pointwise and integral coverings

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Department of Function Theory, Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Street, Moscow, 119991, Russian Federation
Department of Methods of Teaching Mathematics and Computer Science, Karaganda Buketov University, 28 University Street, Karaganda, 100024, Kazakhstan

Department of Function Theory
Department of Methods of Teaching Mathematics and Computer Science

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